It is known that such an elastic tubular body generally takes the form of a cap, closed at one end like a glove finger, or in the form of a sleeve, open at both ends; that such a body is manufactured from an elastic material with dimensions such that it is dilated relative to the natural state (which state it takes on in the absence of external stresses) when it contains within its internal space the elongate member, such that the body tightly fits around the elongate member; and that once it is fitted onto the elongate member, such a body provides air-tightness and water-tightness and/or electrical insulation.
Assemblies are already known comprising such a body and a tubular core for keeping the body expanded, that is to say in a radially dilated state relative to the natural state. The core is thus tightly covered by the tubular body. The internal space of the core is configured to receive internally the elongate member which is to be covered by the protective body.
With such an assembly, the fitting of the protective elastic tubular body onto the elongate member is carried out by inserting the elongate member into the internal space of the core then the core is driven such that it slides both in relation to the elongate member and in relation to the body. As it is no longer supported internally by the core, the body contracts onto the elongate member. When the core is fully extracted, the body tightly covers the elongate member.
PCT Application WO 95/11542 describes such an assembly, comprising:                a protective elastic sleeve; and        a tubular core for keeping the sleeve expanded, which core comprises a first part, which is rigid, and a second part joined end-to-end with the first part, which second part is flexible and turned back to rest on the outside circumferential surface of the first part, the core being configured in order for a pull applied to the first part at the end other than the end by which the first part and the second part are connected, makes the first part slide relative to the second part in an axial movement to attain an extended position in which the whole of the second part extends in line with the first part (the second part no longer has any turned-back portion).        
In this assembly, the second part facilitates the extraction movement of the first part, which does not have to slide directly on the sleeve.
The second part does not stay in the sleeve but is driven out from it with the first part, given that the first part and the second part are joined end-to-end.